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Use of transformed auxiliary variable in estimating the finite population mean. (English) Zbl 0963.62014
Summary: For estimating the finite population mean $$\overline Y$$ of the study character $$y$$, an estimator using a transformed auxiliary variable has been defined. The bias and mean-squared error (MSE) of the proposed estimator have been obtained. The regions of preference have been obtained under which it is better than the usual unbiased estimator $$\overline y$$, the ratio estimator $$\overline y_R=\overline y\overline X/ \overline x$$, the B.V.S. Sisodia and V.K. Dwivedi estimator [J. Ind. Soc. Agricult. Stat. 33, 13-18 (1981)], $$\overline y_s=\overline y(\overline X+ C_x)/(\overline x+C_x)$$, and the H.P. Singh and M.S. Kakran estimator [submitted to ibid.)], $$\overline y_k=y(\overline X+\beta_2(x))/(\overline x+\beta_2(x))$$. An empirical study has been carried out to demonstrate the superiority of the suggested estimator over the others.

##### MSC:
 62D05 Sampling theory, sample surveys
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